no. 2
Heights and the central critical values of triple product L-functions
Compositio Mathematica, Tome 81 (1992) no. 2, pp. 143-209 
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     year = {1992},
     publisher = {Kluwer Academic Publishers},
     volume = {81},
     number = {2},
     mrnumber = {1145805},
     zbl = {0807.11027},
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     url = {https://www.numdam.org/item/CM_1992__81_2_143_0/}
}
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Gross, Benedict H.; Kudla, Stephen S. Heights and the central critical values of triple product $L$-functions. Compositio Mathematica, Tome 81 (1992) no. 2, pp. 143-209. https://www.numdam.org/item/CM_1992__81_2_143_0/

1 A. Beilinson, Higher regulators and values of L-functions, J. Soviet Math. 30 (1985), 2036-2070. | Zbl

2 B.J. Birch, Hecke actions and classes of ternary quadratic forms, preprint. | MR

3 D. Blasius, Critical values of certain tensor product L-functions, Inv. Math. 90 (1987), 181-188. | Zbl

4 S. Bloch, Height pairings for algebraic cycles, J. Pure and Applied Algebra 34 (1984), 119-145. | Zbl | MR

5 W. Casselman, On representations of GL(2) and arithmetic of modular curves, in Modular Forms of One Variable II, Lect. Notes in Math., vol. 349, Springer-Verlag, New York, Heidelberg, Berlin, 1973, 107-141. | Zbl | MR

6 P. Deligne, Formes modulaires et representations de GL(2), Lect. Notes in Math. 349, Springer-Verlag, New York, Heidelberg, Berlin, 1973. | Zbl | MR

7 M. Eichler, Zur Zahlentheorie der Quaternion-Algebren, Crelle J. 195 (1955), 127-151. | Zbl | MR

8 M. Fichler, Quaternaire quadratische Formen und die Riemannsche Vermutung für die Kongruenzzetatfunction, Arch. Math. 5 (1955), 355-366. | Zbl | MR

9 P.B. Garrett, Decomposition of Eisenstein series: Rankin triple products, Ann. of Math. 125 (1987), 209-235. | Zbl | MR

10 P.B. Garrett and M. Harris, Special values of triple product L-functions, preprint (1989). | Zbl | MR

11 S. Gelbart and H. Jacquet, A relation between automorphic forms on GL(2) and GL(3), Ann. Sci. E. N. S. 11 (1978), 471-542. | Zbl | MR | Numdam

12 R. Godement, Notes on Jacquet-Langlands Theory, Institute for Advanced Study, Princeton, N.J., 1970.

13 B.H. Gross, Heights and special values of L-series, CMS Conf. Proc. 7 (1987), 115-187. | Zbl | MR

14 B.H. Gross, S. Kudla and D. Zagier, in preparation (1991).

15 B.H. Gross and C. Schoen, The diagonal on the 3 fold product of a curve, in preparation (1990).

16 B.H. Gross and D. Zagier, Heegner points and the derivatives of L-series, Inv. Math. 84 (1986). | Zbl | MR

17 M. Harris and S. Kudla, The central critical value of a triple product L-function, Annals of Math. 133 (1991), 605-672. | Zbl | MR

18 J. Igusa, Some results on p-adic complex powers, Amer. J. Math. 106 (1984), 1013-1032. | Zbl | MR

19 T. Ikeda, On the functional equations of the triple L-functions, J. Math. Kyoto Univ. 29-2 (1989), 175-219. | Zbl | MR

20 T. Ikeda, On the poles of the triple product L-function, preprint (1990).

21 H. Jacquet and R.P. Langlands, in Automorphic Forms on GL(2), Lect. Notes in Math. 114, Springer-Verlag, New York, Heidelberg, Berlin, 1970. | Zbl | MR

22 H. Jacquet, I.I. Piatetski-Shapiro and J. Shalika, On Euler products and the classification of automorphic representations I, II, Amer. J. Math. 103 (1981), 499-558 and 777-815. | Zbl

23 M. Kashiwara and M. Vergne, On the Segal-Shale-Weil representations and harmonic polynomials, Invent. Math. 44 (1978), 1-47. | Zbl | MR

24 S.S. Kudla and S. Rallis, On the Weil-Siegel formula, J. Reine Angew. Math. 391 (1988), 65-84. | Zbl | MR

25 S.S. Kudla and S. Rallis, A regularized Siegel-Weil formula: the first term identity, in preparation (1990). | Zbl | MR

26 S.S. Kudla and S. Rallis, Poles of Eisenstein series and L-functions, Festschrift in honor of I. Piatetski-Shapiro, Israel Math. Conf. Proc., vol. 3, Weizmann Sci. Press, Israel (1990), 81-110. | Zbl | MR

27 S.S. Kudla and S. Rallis, Degenerate principal series and invariant distributions, Isr. J. Math. 69 (1990), 25-45. | Zbl | MR

28 J.-F. Mestre and J. Oesterle, Elliptic Curves of Prime Conductor, preprint.

29 C. Moeglin and J.-L. Waldspurger, Le spectre résiduel de GL(n), Ann. Sci. E. N. S. 22 (1989), 605-674. | Zbl | MR | Numdam

30 T. Orloff, Special values of mixed weight triple products, Inv. Math. 90 (1987), 169-180. | Zbl | MR

31 I.I. Piatetski-Shapiro and S. Rallis, Rankin triple L-functions, Compositio Math. 64 (1987), 333-399. | Zbl | MR | Numdam

32 D. Prasad, Trilinear forms for GL(2) and local epsilon factors, Compositio Math. 75 (1990), 1-46. | Zbl | MR | Numdam

33 S. Rallis, L-Functions and the Oscillator Representation, Lect. Notes in Math. 1245, Springer-Verlag, New York, Heidelberg, Berlin, 1987. | Zbl | MR

34 S. Rallis, Poles of Standard L functions, Proc. ICM, Kyoto (1990). | Zbl | MR

35 J.-P. Serre, Facteurs locaux des fonctions zeta des varietes algebriques (definitions et conjectures), Sem. DPP 19 (1969). | Zbl | Numdam

36 F. Shahidi, On certain L-functions, Amer. J. Math. 103 (1981), 297-355. | Zbl | MR

37 F. Shahidi, On the Ramanunjan conjecture and finiteness of poles for certain L-functions, Ann. Math. 127 (1988), 547-584. | Zbl | MR

38 F. Shahidi, Third symmetric power L-functions on GL(2), Compositio Math. 70 (1989), 245-273. | Zbl | MR | Numdam

39 G. Shimura, Construction of Class Fields and Zeta Functions of Algebraic Curves, Ann. Math. 85 (1967), 58-159. | Zbl | MR

40 G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton University Press, 1971. | Zbl | MR

41 M.F. Vigneras, Arithmétique des Algèbres de Quaternions, Lect. Notes in Math. 800, Springer-Verlag, New York, Heidelberg, Berlin, 1980. | Zbl | MR

42 A. Weil, Sur certains groupes d'opérateurs unitaires, Acta Math. 111 (1964), 143-211. | Zbl | MR

43 A. Weil, Basic Number Theory, Springer-Verlag, New York, Heidelberg, Berlin, 1974. | Zbl | MR